A note on Kähler-Ricci flow
type: Item
instance of: scholarly article
title: A note on Kähler-Ricci flow
zbMATH Open document ID: 1262.53057
author: Chengjie Yu
published in: Mathematische Zeitschrift
publication date: 2012-10-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/0810.0574
review text: The author considers a complete Kähler-Ricci flow \((M,g(t))\) satisfying Shi's estimate \[ \| \nabla^k Rm \|^2 (x,t) \leq \frac{C(k,s)}{t^k}; \qquad \quad k \in \mathbb N, s \in (0,T), (x,t) \in M \times (0,s], \] where \(T\) is the maximal existence time. Assuming uniform equivalence of \(g(t)\) to \(g(0)\) in the sense that \[ C^{-1} g(0) \leq g(t) \leq C g(0) \] for some given \(C > 0\), the author proves that for any \(k \in \mathbb N\) there exist constants \(A_, B_k\) such that \[ \| \nabla^k Rm \|^2 (x,t) \leq A_k + \frac{B_k}{t^k}, \qquad (x,t) \in M \times [0,T). \] The proof relies on the maximum principle and an induction procedure. An application is given to the long-time existence problem.
reviewed by: Andrea Malchiodi
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 6097139
zbMATH Keywords: Kähler-Ricci flow
zbMATH Keywords: long-time existence
MaRDI profile type: Publication
OpenAlex ID: W2041271518
arXiv ID: 0810.0574
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Wikidata QID: Q125768810
DOI: 10.1007/S00209-011-0929-0
description: scientific article; zbMATH DE number 6097139